# Minimum Uncertainty Wavefunction

1. Sep 13, 2006

### luckymango

Why does one refers to it as a "minimum uncertainty" wavefunction?

2. Sep 14, 2006

### Galileo

The Heisenberg uncertainty principle states $\sigma_x\sigma_p\geq \frac{\hbar}{2}$.
This is an inequality which always holds for any wavefunction. You can make wavefunctions for which $\sigma_x$ and $\sigma_p$ are both pretty big, but you can't make them both arbitrarily small.
You could raise the question for what wavefunction the uncertainty is minimal, that is, when the inequality becomes an equality. This is the minimum uncertainty wavefunction (It turns out be a gaussian.)

3. Sep 18, 2006

### Epicurus

It has, of course, to be a gaussian as qm is a harmoinc theory!